Challenge Overview
This is our second puzzle challenge! We plan to run these puzzles once every month or so. The puzzles can be solved by hand or with the help of a computer. You can reach out in the forums for any questions, but please do not share any ideas or solutions relating to the puzzle itself.
Puzzle
The Collatz sequence is defined as follows. Start with a positive integer n. If n is even then divide it by 2, otherwise multiply it by 3 and add 1. Repeat this process with the new number until you reach a loop. For example if we start with 7 then the sequence will be 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. The number of halving and tripling steps for n to reach 1 is called the total stopping time of n. In the example above the total stopping time is 16. Your task is to find a positive integer with no more than 100 decimal digits that has the largest total stopping time.
The famous Collatz conjecture states that every positive integer will eventually reach 1 when following this process. The conjecture has been shown to be true up to 2^68, but despite decades of effort it still remains unproven for the general case. Perhaps you will be the one to find a counter example to the conjecture?
Submission Guidelines
Submit a single text file with three lines of text. The first line should be your username. The second line should be the number you have found and the third line should be its total stopping time. You can make multiple submissions, but only your last submission will be used for evaluation.
Judging Criteria
A solution will be considered better if it takes more steps to reach 1. The solutions with the largest claimed total stopping time will be verified with a program. Ties will be broken by submission time.
Challenge Schedule
This is a 7 day challenge.